Problem: The following line passes through point $(-9, -4)$ : $y = \dfrac{7}{16} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(-9, -4)$ into the equation gives: $-4 = \dfrac{7}{16} \cdot -9 + b$ $-4 = -\dfrac{63}{16} + b$ $b = -4 + \dfrac{63}{16}$ $b = -\dfrac{1}{16}$ Plugging in $-\dfrac{1}{16}$ for $b$, we get $y = \dfrac{7}{16} x - \dfrac{1}{16}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-9, -4)$